CHAPTER 30 Nuclear - Physics and Astronomy at TAMUpeople.physics.tamu.edu/adair/phys202/CHAPTER 30 Nuclear.pdf · GAMMA – electromagnetic energy A High Energy Photon . 3 NUCLEAR

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CHAPTER 30

RADIOACTIVITY

DISCOVERY – BECQUEREL

DEVELOPMENT – Pierre and Marie Curie

And others

THREE RADIATIONS

ALPHA – nucleus of Helium

BETA - electrons

GAMMA – electromagnetic

2

ALPHA is Nucleus of Helium

BETA PARTICLES are electrons

GAMMA – electromagnetic energy

A High Energy Photon

3

NUCLEAR TRANSMUTATIONS

ALPHA DECAY

�������� �� ℎ� + �ℎ��

�����

���

Masses and Charges must balance

�������� ���

���

��� + �ℎ�����

4

BETA DECAY

�ℎ������� ���� + ����

�����

���

Masses and Charges must balance

�ℎ������� � + ����

������

�����

5

ACTIVITY

NUCLEAR DECAY RATE

NUMBER OF NUCLEAR DECAYS PER

SECOND

ACTIVITY

t

N=

∆

∆

PROPORTIONAL TO NUMBER OF

NUCLEI PRESENT, N

N

t

N∝

∆

∆

6

THEREFORE

N

t

NRATE λ=

∆

∆−=

WHERE λ, THE CONSTANT OF

PROPORTIONALITY, IS THE DECAY

CONSTANT.

Can use calculus to find number of nuclei

(N) as function of time.

7

teNN

λ−= 0

START WITH N0 NUCLEI WILL HAVE

AFTER TIME t N.

8

HALF LIFE

IF YOU START WITH N0 NUCLEI HOW

MUCH TIME WILL IT TAKE TO ONLY

HAVE HALF THAT NUMBER?

THAT WILL BE CALLED THE HALF-

LIFE.

START WITH N0

WHEN WILL HAVE 2

0N

9

2/1

00

2

teN

N λ−=

SOLVE FOR t1/2

2/1

2

1 te

λ−=

10

λ2

1ln

2/1

−

=t

λ

693.02/1 =t

2/12

1ln tλ−=

11

Insert FIGURE 30.6

EXAMPLE

If a radioactive material initially contains

3.00 mg of U234

92 , how much will remain

unchanged after 62,000 years? (For U234

92

t1/2 = 2.48 x 105 y and λ = 8.88 x 10

-14 s

-1.)

teNN

λ−= 0

( ) atomsxg

atomsxxgxN

1823

3

0 1072.7234

1002.61000.3 == −

12

173.0102.61048.2

693.0 4

5 == yxxyx

tλ

THEREFORE

173.0181072.7 −= eXN

13

atomsXN1810494.6=

MASS = ?

( ) gxatomsx

gxatomsxm

3

23

18 1052.21002.6

23410494.6 −==

WHAT IS THE ACTIVITY OF THIS

SAMPLE?

N

t

NRATE λ=

∆

∆−=

14

( ) ( )atomsXxsxNt

N 18114 10494.61088.8 −−−=−=∆

∆λ

sdisxNt

N/1076.5 5−=−=

∆

∆λ

15

DECAY SERIES

HAVE SEEN

������

������� �� ℎ� + �ℎ��

���

And

�ℎ�����

������� ���� + ����

���

16

WE CAN FOLLOW A SERIES -

Uranium 238 SERIES

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MOST RADIOACTIVE NUCLEI ARE

IN ONE OF 4 SERIES

�������� ����

�����

���

�ℎ������� ����

�����

���

�������� ����

�� ��

��!

�"������� #$��

�����

���

18

NOTE THAT NO SERIES DECAYS TO

�������

IF AT TIME IN HISTORY MOLTEN

LEAD SOLIDIFIED THERE WOULD

BE A MIXTURE OF Pb ISOTOPES.

WHEN IT SOLIDIFIED FOR

EXAMPLE

%&'(

()*

%&'(()+ = -./�0��"�

WITH TIME ������� INCREASES

19

AND THUS

�������

�������

123456757

THIS GIVES A METHOD OF

DETERMINING TIME SINCE

SOLIDIFICATION

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21

ANOTHER AGE DATING METHOD

CARBON 14 DATING

CARBON 12 IS THE MOST

ABUNDENT ISOTOPE OF CARBON

AND IS STABLE

CARBON 14 IS UNSTABLE AND

DECAYS TO NITROGEN (A GAS)

3������� 2 + ����

���

��

WITH HALF-LIFE OF 5730 YEARS

22

23

OVER TIME RATIO LIVING PLANTS

AND ANIMALS

8*

9+

8*9( = 3:27�62�;6<�5

FROM TIME OF DEATH ON

3������� 2 + ����

���

��

24

AND THEREFORE

8*

9+

8*9( = =�>?��-�-

MEASURE RATIO OF CARBON 14

TO CARBON 12 AND DETERMINE

YEARS SINCE DEATH OF PLANT OR

ANIMAL.

25

FISSION

@ + ����������

��! �������� A? + �� + 3@!�

�������

�����

26

27

28

FUSION

� + �������� � + C + DE = 0.42J�;�

��� �

�

Then

� + �������� ���

� + KE = 5.49J�;��

��

Then

���� + ��

������� �� + � + ��

� ��

��

��

With E = 12.86J�;

29

Can only take place at high temperature

and high pressure.

In Sun

Or Maybe Some Day

30

FUNDAMENTAL PARTICLES AND

FORCES

FOUR FORCES FOUND IN NATURE

1. The Strong Interaction

2. The electromagnetic interaction

3. The weak interaction

4. The gravitational interaction

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PARTICLES

Leptons

32

Hadrons

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Quarks